#3 Find the line equation(s) of the line(s) through point P(1, 0, 1) that meets the following line at point(s) at distance 3 from point Po(1, 2, 0). L:
#3 Find the line equation(s) of the line(s) through point P(1, 0, 1) that meets the following line at point(s) at distance 3 from point Po(1, 2, 0). L:
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
Find the line equation(s) of the line(s) through point P (1, 0, 1) that meets
the following line at point(s) at distance 3 from point P0(1, 2, 0).
![**Problem #3:**
Find the equation(s) of the line(s) passing through the point \( P(1, 0, 1) \) that intersect the given line at a distance of 3 from the point \( P_0(1, 2, 0) \).
The line \( L \) is defined by the parametric equation:
\[
L: \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 1 \\ 2 \\ 0 \end{bmatrix} + t \begin{bmatrix} 2 \\ -1 \\ 2 \end{bmatrix}
\]
where \( t \) is a parameter.
**Explanation of the Parametric Equation:**
- The line \( L \) is described in vector form, where:
- \(\begin{bmatrix} 1 \\ 2 \\ 0 \end{bmatrix}\) represents a point on the line.
- \(\begin{bmatrix} 2 \\ -1 \\ 2 \end{bmatrix}\) is the direction vector of the line.
- As \( t \) varies, it generates different points along the line.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff90e9f76-a8ee-4e86-857e-4cb9f0bb2381%2F38257a12-533c-41e9-b1c7-d9c618f958a7%2F1e5l4qm_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem #3:**
Find the equation(s) of the line(s) passing through the point \( P(1, 0, 1) \) that intersect the given line at a distance of 3 from the point \( P_0(1, 2, 0) \).
The line \( L \) is defined by the parametric equation:
\[
L: \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 1 \\ 2 \\ 0 \end{bmatrix} + t \begin{bmatrix} 2 \\ -1 \\ 2 \end{bmatrix}
\]
where \( t \) is a parameter.
**Explanation of the Parametric Equation:**
- The line \( L \) is described in vector form, where:
- \(\begin{bmatrix} 1 \\ 2 \\ 0 \end{bmatrix}\) represents a point on the line.
- \(\begin{bmatrix} 2 \\ -1 \\ 2 \end{bmatrix}\) is the direction vector of the line.
- As \( t \) varies, it generates different points along the line.
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